Debye model ↩

Metadata

aliases: []
shorthands: {}
created: 2021-11-04 16:45:10
modified: 2022-01-10 04:13:03

The Debye model gives us a simple dispersion relation for approximating lattice vibrations in crystal lattices.
The dispersion relation given is:

Where is a constant speed of sound and it works up until the Debye frequency. It gives a good approximation for the dispersion branches of small wavenumbers.

The phonon state density in the Debye model

In 1D

For sample length :

Does not depend on the frequency.

In 2D

For sample area :

Linearly depends on the frequency.

In 3D

For sample volume :

Depends on the frequency quadratically.

Determining the Debye frequency

The usual way of determining the Debye frequency is to have the number of modes equal to the number of unit cells in the sample.